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 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Lagrange points? 01/28/11 at 11:42:18   I guess this is more a science question, but if I can simulate it in GS then all the better   For the SF background I'm working on, I want to have 'jump points' located at the L4 and L5 points of the most massive objects in a planetary system. This has a few implications:   1) If there are no planets in the system, then it contains no jump points at all. This is OK, but I'm wondering what happens if you just have a system full of dust and rocks - would there be any L4/L5 points in there? If the only massive object of note was a small 10-100km diameter asteroid that had 'cleared out its orbit', would its lagrange points be stable at all? What would be the smallest object that can have stable L4/L5 points? I'm figuring that the jump points themselves are massless objects, but at really small scales I guess the mass of the spaceship itself might disrupt things!   2) If there were no planets, but multiple stars (e.g. a Binary or trinary system) then you wouldn't have L4/L5 points unless the mass ratio of the stars was below about 25:1 (so in most cases they'd be unstable you had a very massive star and a low mass star, such as a 10 solar mass star and a 0.4 solar mass star, which would be unlikely).     3) In a solo or multiple system containing planets, the jump points would be found at the L4/L5 points of the most massive planet in the system. The jump points can exist in a system as long as stable L4/L5 points are located anywhere within it.     How could I test this in GS? I'm not sure how one makes an object orbit an L4/L5 point, do I just create the lagrangian object with the same orbital parameters as the planet but with a mean anomaly of +60 or -60 degrees relative to the planet? (I guess it might drift a bit and go into an orbit around the L4/L5 point over time?). And if I put other planets in different orbits in the system, would they affect the stability of the L4/L5 points? Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Lagrange points? Reply #1 - 01/28/11 at 14:22:26   Quote from EDG on 01/28/11 at 11:42:18:How could I test this in GS? I'm not sure how one makes an object orbit an L4/L5 point, do I just create the lagrangian object with the same orbital parameters as the planet but with a mean anomaly of +60 or -60 degrees relative to the planet?   I guess not, since if I do that I get two objects in the same orbit, with one 60 behind of the other, but if I switch it to a view centred on the planet then I just see the lagrange object orbiting the stationary planet (on an interior orbit relative to the sun). I suppose the problem is that I have no idea how to do those nice lagrange animations that others do here. Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1057 Gender: Re: Lagrange points? Reply #2 - 01/28/11 at 15:49:21   It should work if you create objects 60 +- from a massive body.  Create all three of the objects at the same time though.  Don't look at your planet's mean anomoly in the Orbital Elements interface and add or subtract 60 from that.  The problem is that mean anomoly is measured from the ascending node, and if your planet is orbiting in the ecliptic then there is no ascending node, and mean anomoly is arbitrairly reported.   I don't think there's any lower limit to the mass of the planet.  But the lower it gets, the more likely that other bodies will perturb your objects out of L4/5.  In a 2-body system (2 bodies with mass) and 2 more massless bodies, there should be no lower limit as long as you maintain a ratio greater than about 25:1 Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Lagrange points? Reply #4 - 01/28/11 at 17:18:56   Quote from Tony on 01/28/11 at 15:49:21:It should work if you create objects 60 +- from a massive body.  Create all three of the objects at the same time though.  Don't look at your planet's mean anomoly in the Orbital Elements interface and add or subtract 60 from that.  The problem is that mean anomoly is measured from the ascending node, and if your planet is orbiting in the ecliptic then there is no ascending node, and mean anomoly is arbitrairly reported.   How do I create the objects though (especially if I have a circular, non-inclined orbit)? Would you be able to write a walkthrough for me please, because I'm not seeing how to create them all at the same time as you describe. Back to top (formerly known as Mal)   IP Logged
 phoenixshade Uploader Proud to be an Ape Posts: 26 Gender: Re: Lagrange points? Reply #5 - 01/28/11 at 18:03:05   Screencaps. Create a new sim and make sure it is paused.   For the planet, set Longitude of Node, Argument of Periapsis (Periapsis = perifocus and is the term I prefer, since an ellipse technically has two foci), and Mean Anomaly all to zero. Make sure all random elements are also set to zero:     For the orbiter, same, only Mean Anomaly is 60:     That's pretty much it... although I do have to make a slight correction to what Tony said above: Mean anomaly is measured from the periapsis, not from the ascending node. So at a mean anomaly of 0, the object is at its closest approach to the central body; at mean anomaly of 180, it is at its farthest. The argument of periapsis is itself measured from the longitude of the ascending node. It took me a while to get that down, and until you do it can be pretty difficult to position objects exactly where you want them. Back to top IP Logged
 Tony YaBB Administrator Posts: 1057 Gender: Re: Lagrange points? Reply #6 - 01/28/11 at 18:25:51   Quote from phoenixshade on 01/28/11 at 18:03:05: ... although I do have to make a slight correction to what Tony said above: Mean anomaly is measured from the periapsis, not from the ascending node...   Oops   .  It still makes for an ambiguous situation when your orbit is circular.  So you need to create all your objects at the same time if you set ecc=0. Back to top IP Logged
 Tony YaBB Administrator Posts: 1057 Gender: Re: Lagrange points? Reply #7 - 01/28/11 at 19:14:35   Just for fun, try the following: File > New   Zoom out until the screen with is about 3-4 AU   Pause the simulation   Objects > Create Objects   Mass: 1 Jupiter mass, SMA: 1 AU, MA: 0, set all random stuff to 0%   Press Create   Objects > Create Objects   Number of objects 5   Press the SMA distribution until you see the words (Start, End)   Enter 0.98, 1.02   MA: 60   Press Create   If desired, repeat previous 6 steps, except MA: 300   View > Rotating Frame Adjustment.  Choose the object with 1 Jupiter mass.  Select rotating frame.   Preferences > Graphic Output 50   Save the simulation   Unpause and watch Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Lagrange points? Reply #8 - 01/28/11 at 19:37:58   Quote from phoenixshade on 01/28/11 at 18:03:05:Screencaps. Create a new sim and make sure it is paused. For the planet, set Longitude of Node, Argument of Periapsis (Periapsis = perifocus and is the term I prefer, since an ellipse technically has two foci), and Mean Anomaly all to zero. Make sure all random elements are also set to zero:   Thanks! Though actually I did exactly what you said here!     Maybe I'm just not displaying it properly. It's quite likely that I'm not understanding how "Rotating Frame" works.     Oh, I followed tony's instructions (though for an earthlike planet and a small mass)  and got a planet and a lagrange orbiter that were two dots sitting there 60 degrees apart around the sun, which is promising. I guess as phoenix says, not much is going to happen with this since there are no perturbers.     So how does this "rotating frame adjustment" thing work exactly? Is there any documentation describing it? Back to top (formerly known as Mal)   IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Lagrange points? Reply #9 - 01/28/11 at 19:55:42   Quote from Tony on 01/28/11 at 19:14:35:Just for fun, try the following:   I presume the lagrange objects should be very small/low mass, right?     Interesting... they're spreading out!   Oh, ha! Now it looks like they're orbiting the lagrange point (in one of those long tadpole orbits)!   That's cute . Looks like I have something new to play with Back to top (formerly known as Mal)   IP Logged
 phoenixshade Uploader Proud to be an Ape Posts: 26 Gender: Re: Lagrange points? Reply #10 - 01/28/11 at 20:13:51   The rotating frame is great for looking at motions relative to a particular planet. (Case in point: the Lagrange objects we're talking about here.) What it does is rotates the camera. You can either specify the period of rotation (using the numeric field) or you can select any object in your sim and it will rotate the camera in sync with that object's orbit. Almost all orbits with resonances are more interesting this way. In fact, objects that otherwise seem mundane can have some very interesting properties that only become noticeable in a rotating frame.   Besides adding perturbers or Tony's example varying the SMA, try giving the planet a small eccentricity (around 0.05-0.08 is good) but put the lagrange objects in circular orbits, and view this in a rotating frame using the planet's period. Over time, the lagrange objects will start to develop eccentricity as well and start the looping motion characteristic of Trojan asteroids. I am pretty sure that the langrange object's eccentricity will end up very slowly oscillating over the range 0 – 2e (where e is the eccentricity of the planet).   Trust me, once you really start exploring the nuances of 1:1 resonances (and other resonances as well), you'll keep coming back to them. They are fascinating. Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Lagrange points? Reply #11 - 01/29/11 at 11:28:38   Quote from phoenixshade on 01/28/11 at 20:13:51:The rotating frame is great for looking at motions relative to a particular planet. (Case in point: the Lagrange objects we're talking about here.) What it does is rotates the camera. You can either specify the period of rotation (using the numeric field) or you can select any object in your sim and it will rotate the camera in sync with that object's orbit. Almost all orbits with resonances are more interesting this way. In fact, objects that otherwise seem mundane can have some very interesting properties that only become noticeable in a rotating frame.   So what does changing the focus object do? If I focus on Jupiter in Tony's sim, that doesn't have it so that the camera is rotating in sync with the object's orbit, it centres the view on the planet instead, but it produces a very different view to the rotating one.     Quote:Besides adding perturbers or Tony's example varying the SMA, try giving the planet a small eccentricity (around 0.05-0.08 is good) but put the lagrange objects in circular orbits, and view this in a rotating frame using the planet's period. Over time, the lagrange objects will start to develop eccentricity as well and start the looping motion characteristic of Trojan asteroids. I am pretty sure that the langrange object's eccentricity will end up very slowly oscillating over the range 0 – 2e (where e is the eccentricity of the planet).   I'm wondering what happens to the lagrange points if the planet's orbit is eccentric (e.g. e=0.5 or more). Are they still stable?     And is there a way to enter the L1/L2/L3 points too? It'd be nice if there was an option in the program to just place objects there to save us having to calculate the locations ourselves first.     Quote:Trust me, once you really start exploring the nuances of 1:1 resonances (and other resonances as well), you'll keep coming back to them. They are fascinating.   Oh definitely Back to top (formerly known as Mal)   IP Logged